Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-4732.2-e
Conductor 4732.2
Rank \( 0 \)

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Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 4732.2-e over \(\Q(\sqrt{-7}) \)

Isogeny class 4732.2-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
4732.2-e1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1938 a + 467\) , \( 34770 a - 41587\bigr] \)
4732.2-e2 \( \bigl[1\) , \( -1\) , \( 1\) , \( 1938 a - 1471\) , \( -34770 a - 6817\bigr] \)
4732.2-e3 \( \bigl[1\) , \( -1\) , \( 1\) , \( 866\) , \( 6445\bigr] \)
4732.2-e4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -4254\) , \( 59693\bigr] \)
4732.2-e5 \( \bigl[1\) , \( -1\) , \( 1\) , \( -31294\) , \( -2081875\bigr] \)
4732.2-e6 \( \bigl[1\) , \( -1\) , \( 1\) , \( -59134\) , \( 5547693\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 4 & 8 & 8 \\ 4 & 1 & 2 & 4 & 8 & 8 \\ 2 & 2 & 1 & 2 & 4 & 4 \\ 4 & 4 & 2 & 1 & 2 & 2 \\ 8 & 8 & 4 & 2 & 1 & 4 \\ 8 & 8 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph